Fluid lens assembly

ABSTRACT

A non-round fluid lens assembly includes a non-round rigid lens and a flexible membrane attached to the non-round rigid lens, such that a cavity is formed between the non-round rigid lens and the flexible membrane. A reservoir in fluid communication with the cavity allows a fluid to be transferred into and out of the cavity so as to change the optical power of the fluid lens assembly. In an embodiment, a front surface of the non-round rigid lens is aspheric. Additionally or alternatively, a thickness of the flexible membrane may be contoured so that it changes shape in a spheric manner when fluid is transferred between the cavity and the reservoir.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation application of U.S. patentapplication Ser. No. 13/404,914, filed Feb. 24, 2012, which is acontinuation of Ser. No. 12/579,203, filed Oct. 14, 2009, now U.S. Pat.No. 8,136,942, the disclosures of which are hereby incorporated hereinby reference in their entirety.

BACKGROUND

1. Field

Embodiments of the present invention relate to fluid-filled lenses, inparticular variable fluid-filled lenses.

2. Related Art

Basic fluid lenses have been known since about 1958, as described inU.S. Pat. No. 2,836,101, incorporated herein by reference in itsentirety. More recent examples may be found in “DynamicallyReconfigurable Fluid Core Fluid Cladding Lens in a MicrofluidicChannel,” Tang et al., Lab Chip, 2008, vol. 8, p. 395, and in WIPOpublication WO2008/063442, each of which is incorporated herein byreference in its entirety. These applications of fluid lenses aredirected towards photonics, digital telephone and camera technology, andmicroelectronics.

Fluid lenses have also been proposed for ophthalmic applications. (See,e.g., U.S. Pat. No. 7,085,065, incorporated herein by reference in itsentirety.) In all cases, the advantages of fluid lenses-including a widedynamic range, ability to provide adaptive correction, robustness, andlow cost—have to be balanced against limitations in aperture size,tendency to leak, and consistency in performance. The '065 patent, forexample, has disclosed several improvements and embodiments directedtowards effective containment of the fluid in the fluid lens to be usedin ophthalmic applications. Power adjustment in fluid lenses has beeneffected by injecting additional fluid into a lens cavity, byelectrowetting, by application of ultrasonic impulse, and by utilizingswelling forces in a cross-linked polymer upon introduction of aswelling agent to the lens fluid, such as water.

In all cases, there are several key limitations in current fluid lenstechnology that need to be overcome to optimize the commercial appeal ofthis technology. For example, the thickness of fluid lenses is generallygreater than conventional lenses of the same power and diameter.Additionally, it is not currently possible to provide a variation ofspherical power as well as astigmatism across the lens optic using fluidlens technology. Nor is it currently possible to make fluid lenses inany desired shape other than a round shape because of complicationsintroduced in non-uniform expansion of non-round fluid lenses.

BRIEF SUMMARY

In an embodiment of the present invention, a non-round fluid lensassembly includes a non-round rigid lens and a flexible membraneattached to the non-round rigid lens, such that a cavity is formedbetween the non-round rigid lens and the flexible membrane. A reservoirin fluid communication with the cavity allows a fluid to be transferredinto and out of the cavity so as to change the optical power of thefluid lens assembly. In an embodiment, a front surface of the non-roundrigid lens is aspheric. Additionally or alternatively, a thickness ofthe flexible membrane may be contoured so that it changes shape in aspheric manner when fluid is transferred between the cavity and thereservoir.

Additionally or alternatively, the flexible membrane may have an “inset”portion that is more flexible than other portions of the flexiblemembrane, such that transfer of the fluid between the cavity and thereservoir causes the shape of the inset portion to change in a sphericalmanner without substantially changing portions of the flexible membraneother than the inset portions. In an embodiment, the inset portion iselliptical in shape. The inset portion may be contoured so that itchanges shape in a spheric manner when fluid is transferred between thecavity and the reservoir. Including such an inset portion in theflexible membrane allows a non-round lens (e.g., an oval-shaped,rectangular-shaped, or other-shaped lens that may be preferred by awearer) to be worn while maintaining the advantages of a fluid-filledlens.

Further embodiments features, and advantages of the present invention,as well as the structure and operation of the various embodiments of thepresent invention, are described in detail below with reference to theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES

The accompanying drawings, which are incorporated herein and form a partof the specification, illustrate the present invention and, togetherwith the description, further serve to explain the principles of theinvention and to enable a person skilled in the pertinent art to makeand use the invention.

FIG. 1 is a diagram of an exemplary fluid-filled lens assembly,according to an embodiment of the present invention.

FIG. 2 shows the variation of astigmatism as a function of eccentricityin a fluid-filled lens assembly without correction to a front lenssurface.

FIG. 3 shows the variation of astigmatism as a function of eccentricityin a fluid-filled lens assembly having a toric front lens surfacecorrection, according to an embodiment of the present invention.

FIG. 4 illustrates deformation of a flexible membrane in a fluid lens,according to an embodiment of the present invention.

FIGS. 5a,b and 6 a,b illustrate contoured flexible membranes, accordingto embodiments of the present invention.

FIGS. 7a,b illustrate an exemplary elliptical inset in a fluid lensassembly, according to an embodiment of the present invention.

FIGS. 8a,b illustrate deformation of a flexible membrane in a fluidlens, according to an embodiment of the present invention.

The present invention will be described with reference to theaccompanying drawings. The drawing in which an element first appears istypically indicated by the leftmost digit(s) in the correspondingreference number.

DETAILED DESCRIPTION

While specific configurations and arrangements are discussed, it shouldbe understood that this is done for illustrative purposes only. A personskilled in the pertinent art will recognize that other configurationsand arrangements can be used without departing from the spirit and scopeof the present invention. It will be apparent to a person skilled in thepertinent art that this invention can also be employed in a variety ofother applications.

It is noted that references in the specification to “one embodiment”,“an embodiment”, “an example embodiment”, etc., indicate that theembodiment described may include a particular feature, structure, orcharacteristic, but every embodiment may not necessarily include theparticular feature, structure, or characteristic. Moreover, such phrasesare not necessarily referring to the same embodiment. Further, when aparticular feature, structure, or characteristic is described inconnection with an embodiment, it would be within the knowledge of oneskilled in the art to effect such feature, structure, or characteristicin connection with other embodiments whether or not explicitlydescribed.

The limitations of previously-available fluid-filled lens technologydescribed in the Background section above may be removed by constructingan aspheric fluid lens. Previous fluid lenses have always been round inshape, since no method existed to construct an aspheric fluid lens. FIG.1 illustrates an exemplary aspheric fluid lens 100 according to anembodiment of the present invention. Fluid lens 100 includes a rigidfront surface 118, a flexible back surface 104, and a fluid filling thecavity 106 formed between front surface 118 and back surface 104. Rigidfront surface 118 may be provided by a rigid optical lens 108 made of,for example, glass or plastic. Flexible back surface 104 may be providedby, for example, a flexible membrane 110 stretched flat over the edge ofrigid optical lens 108. The fluid lens formed thereby is connected via achannel 112 to a reservoir 114 lined or otherwise formed from with anelastomeric deformable membrane that contains excess fluid. Fluid lens100 and reservoir 114 together form a sealed unit. An actuator 116 isoperable to squeeze or expand the deformable membrane inside thereservoir to transfer fluid between reservoir 114 and fluid lens 100through channel 112. Actuator 116 may be, for example and withoutlimitation, a bulb actuator, a syringe-type actuator, or a dialactuator. In embodiments, neither, either, or both of rigid optical lens108 and flexible membrane 110 can have optical power. Channel 112,connecting fluid lens 100 to reservoir 114, may be housed, for example,in the eye piece of an eyeglass frame or temple pieces of an eyeglassframe.

Throughout this disclosure, the term “fluid lens assembly” will be usedto describe the assembly of rigid front lens 108, flexible membrane 110,and the intervening fluid transfer system including channel 112 andreservoir 114. The term “fluid lens” will be used to denote the fluidlayer and the two surfaces 102 and 104 containing the fluid and formingthe surfaces of the fluid lens.

In non-round fluid lenses, the pressure of the fluid causes differentdeflections of the flexible membrane along its short and long axes, andthus produces a non-spherical deflection of the membrane. Non-roundfluid lenses of embodiments of the present invention therefore correctfor the astigmatism created by this deflection. In one embodiment, thefront surface of the rigid front lens corrects for the astigmatismcaused by the fluid. Additionally or alternatively, a thickness of theflexible membrane may be contoured so as to effect a sphericaldeflection of the membrane in response to fluid pressures. In anembodiment, the flexible membrane includes an inset portion that is moreflexible than other portions of the flexible membrane, such thattransfer of the fluid between the cavity and the reservoir causes theshape of the inset portion to change in a spherical manner withoutsubstantially changing portions of the flexible membrane other than theinset portions.

Aspherization of the Front Lens

A fluid lens, such as fluid lens 100, may be rendered aspheric byproviding an aspheric front (rigid) lens. Since front lens 108 is incontact with the fluid at its back surface 102, the impact of addingaspheric correction to back surface 102 of front lens 108 will beattenuated by the refractive index of the fluid relative to therefractive index of the front lens material. Indeed, the change in thethickness of front lens 108 needed to provide an aspheric correctionthrough back surface 102 may be expressed as:

$\begin{matrix}{d = {d_{1}\frac{n_{1} - 1}{n_{1} - n_{2}}}} & \left( {{Eq}.\mspace{14mu} 1} \right)\end{matrix}$

in which d is the local change in thickness of the front lens requiredto provide a particular change in optical power at that point, d₁ is thechange in thickness that would be necessary if the fluid had been air,n₁ is the refractive index of the front lens material and n₂ is therefractive index of the fluid. For example, if front lens 108 is made ofPolycarbonate of bisphenol A and the fluid is silicone oil, then n₁ is1.59 and n₂ is 1.54, resulting in d equal to 11.8d₁. In other words, arelatively large variation in lens thickness will be required to providean aspheric correction, if that correction is added to back surface 102of front lens 108.

Lens thickness may be reduced by adding an aspheric correction to afront surface 118 of front lens 108, front surface 118 being in contactwith air. The aspheric correction to front surface 118 may be in theform of rotationally symmetrical aspheric correction, rendering thesurface of rigid lens 108 ellipsoidal or hyperboloidal. In this case,the surface may be described by Eq. 2, in which the surface isellipsoidal if p is positive, and hyperboloidal if p is negative:

$\begin{matrix}{X = \frac{y^{2}}{r_{0} + \sqrt{\left( {r_{0}^{2} - {py}^{2}} \right)}}} & \left( {{Eq}.\mspace{14mu} 2} \right)\end{matrix}$

Rotationally symmetric aspheric corrections applied to front surface 118of rigid lens 108 provide at least two benefits. Aspheric correctionsmay be designed to minimize spherical aberration present in the fluidlens that may be especially noticeable for high spherical powers.Additionally, the plus power of the fluid lens may be reduced at highgaze angles, consistent with visual needs of the wearer.

Toric Correction of the Front Lens

Additionally or alternatively, other aspheric corrections may be appliedto front surface 118 of rigid lens 108. For example, surface 118 may berendered toroidal. The astigmatism thereby added to front surface 118 ofrigid lens 108 has at least two benefits. The astigmatism may be used toneutralize the natural astigmatism of the eye, possessed by about 80% ofthe population requiring vision correction. The astigmatism may also beused to neutralize the astigmatism generated on surface 104 of flexiblemembrane 110 when the shape of the fluid lens deviates from a circle.

Persons having natural astigmatism in their eyes typically wearastigmatic correcting eyeglasses to achieve best corrected vision. Forthis correction to be applicable, the direction of the astigmatic axisof the lens has to be orthogonal to the astigmatic axis of the eye ofthe wearer of the eyeglasses. If this astigmatic correction is providedby adding a toric curve to front surface 118 of rigid lens 108, then itis desired to make front toric rigid lenses 108 with the toric axis atall possible angles relative to the 0-180° line of rigid lens 108. Thiswould constitute 180 different configurations, or skus. This is becausethe fluid lens assembly is not rotationally symmetrical, since itincludes channel 112 attached to fluid lens 100. Additionally, it isdesirable to substantially match the magnitude of the astigmaticcorrection added to front surface 118 of rigid lens 108 to the magnitudeof the astigmatic correction required by the wearer. While the totalrange of magnitudes of natural astigmatism is very large (approximately0 to approximately 15 diopters, or more), it is about 6 diopters (D) for99% of the population requiring vision correction. Since the matchbetween the natural astigmatism of the eye and the correctingastigmatism of the lens is required to be to the nearest 0.25 D, about25 different configurations of the front surface are required to coverthe range mentioned above. Also, the attachment of channel 114 to rigidlens 108 leads to a differentiation between left and right lenses,multiplying the total number of skus by a further factor of two.Therefore, 9,000 different configurations on front surface 118 of rigidlens 108 may be needed to provide correction to 99% of the populationrequiring vision correction.

In an embodiment of the present invention, it is possible tosubstantially reduce the number of skus on the front lens by designing arotationally symmetrical lens blank that may be molded or machined inhigh volume. The desired lens shape may then be cut out to correspond tothe desired shape of the fluid lens, and the membrane bonded to theouter edge of this shape that has been cut out. A hole may be drilledinto the side of the rigid lens that has been cut out to provide aconnection to the fluid path inside the channel. A small connector or asleeve may connect the end of the channel to the hole.

Application of a toric correction to front surface 118 of rigid lens 108of the fluid lens assembly also enables construction of fluid lensesthat are non-round (e.g., oval or rectangular) in shape. Non-round fluidlenses have not been commercialized because a non-round fluid lensdevelops astigmatic error as the fluid lens is inflated to reach ahigher plus power. This is because injection of fluid into a fluid lenscauses an increase in hydrostatic pressure that is equal in alldirections. This force causes the flexible membrane (such as membrane110) of the fluid lens assembly to stretch or bulge outwards. Moreover,the force renders the surface of the membrane more convex and gives thefluid lens a higher plus power. In the case of a non-round fluid lens,the length of the meridians of the membrane are not equal in alldirections. The curvature of the membrane is therefore different indifferent meridians, being steepest in the shortest meridian and leaststeep along the longest meridian. This leads to a toric shape. In anembodiment, it is possible to neutralize this inflation-inducedastigmatism in the fluid lens by adding an astigmatic correction to thefront surface of the rigid lens. In this approach, when the fluid lensis not inflated (i.e., when it is at its lowest plus power), the lensassembly has astigmatism corresponding to the astigmatism added to thefront surface of the rigid lens. That is, when the fluid lens is notinflated, the astigmatism added to the front surface of the rigid lensis uncompensated by any inflation-induced astigmatism. Addition ofastigmatism to front surface 118 of rigid lens 108 enables a trade-offbetween astigmatism at the lowest plus power and astigmatism at higherplus powers. This trade-off may be computed and optimized for the totaldesigned range of powers of the fluid lens. Such a trade-off may also beacceptable to the wearer, provided that the astigmatism does not exceedthe threshold of tolerance of astigmatism of the human eye at any pointin the range or powers of the fluid lens.

In one exemplary embodiment, a fluid lens is designed according to theparameters shown in Table 1. The front surface of the fluid lens doesnot have any astigmatic correction in this embodiment.

TABLE 1 Specifications of a fluid lens embodiment Radius of curvature ofthe front surface of the rigid 500 mm lens, R_(a) Radius of curvature ofthe back surface of the rigid 500 mm lens, R_(b) Long diameter of thefluid lens, a 35.0 mm Short diameter of the fluid lens, b 34.0 mmEccentricity, a/b 0.972 Range of fluid lens operation 1.25 D to 3.25 DInitial power along the long axis, DI_(a) 1.25 D Initial power along theshort axis, DI_(b) 1.26 D Astigmatism in the initial state of the fluidlens 0.01 D Final power along the long axis of the fluid lens, DF_(a)3.25 D Final power along the short axis of the fluid lens, DF_(b) 3.37 DAstigmatism in the final state of the fluid lens 0.12 D

In the fluid lens embodiment described in Table 1, the rigid lens ismade of Polycarbonate of Bisphenol A, the membrane is biaxially orientedpolyethylene terephthalate (trade name MYLAR), and the fluid is asilicone oil of refractive index 1.54. In this case, the degree ofdeparture from the round shape is expressed as the eccentricity, and theshape becomes progressively more non-round as it departs father from1.0. The data in Table 1 shows that the slight departure from a roundshape has caused the development of a relatively low amount ofastigmatism (0.12 D) at the highest point of the range, i.e., 3.25 D.

FIG. 2 shows the dependence of the buildup of astigmatism as a functionof eccentricity in this fluid lens embodiment. The ordinate showsastigmatism in diopters (D), while eccentricity (k_(v)) has been plottedon the x axis. In FIG. 2, line 202 represents the fluid lens embodimentdescribed in Table 1. Line 204 shows the values of astigmatism at thelowest point of the range (1.25 D), while line 206 represents thehighest point of the range (3.25 D).

It is clear that for noticeably (that is, commercially useful) non-roundgeometries of the fluid lens, e.g, k_(v)<0.85, the relatively smallinflation required to reach the lowest point of the power range (1.25 D)leads to a small magnitude of astigmatism. This astigmatism is mostlybelow the level of perception of the human eye (typically 0.10-0.12 D).However, the induced astigmatism at the higher end of the power rangereaches 0.85 D at k_(v)=0.85, well above the range of tolerance ofastigmatism by the human eye when engaged in near vision tasks, which istypically about 0.50 D at direct gaze (i.e., gaze angle of 0° and nomore than 0.75 D over any part of the lens beyond gaze angle of 15°).FIG. 2 demonstrates the magnitude of the problem associated withnon-round fluid lenses.

FIG. 3 shows the rate of development of astigmatism in the fluid lensembodiment specified in Table 1 with an added astigmatic correction(i.e., toric correction) of 0.125 D on the front surface of the rigidlens. Line 304, which represents the values of astigmatism at the lowestpoint of the range, reaches 0.125 D at an eccentricity of 1.0, in accordwith the design intent. Line 306, which represents the values ofastigmatism at the highest point of the range, reaches the value of0.501) at an eccentricity of 0.87. Interestingly, the astigmatism of thefluid lens remains constant at about 0.121) over the whole range ofpowers at an eccentricity of 0.94. It is possible to reach non-roundshapes of lower eccentricity by increasing the astigmatic correction ofthe front surface of the rigid lens. The maximum such correction shouldnot exceed 0.18 D, consistent with visual comfort and image qualityexpected by wearers at the low end of the power range of the fluid lensassembly. This result shows that it is possible to design fluid lensesthat are moderately non-round in shape with this approach.

Modification of the Flexible Membrane

A fluid lens, such as fluid lens 100, may be rendered aspheric byallowing the membrane, such as membrane 110, to inflate to adopt anaspheric (as opposed to spherical) shape. In an embodiment, an asphericfluid lens uses a membrane of contoured thickness to form the fluidlens. A membrane of uniform thickness used to form a fluid lens assemblycircular in shape inflates uniformly, thereby acquiring a sphericalshape. The local deflection of the membrane is mainly controlled by thelocal rigidity of the membrane, and can be altered by stiffening themembrane or altering its thickness across the surface. A membrane ofcontoured thickness may therefore be used to form an aspheric fluidlens.

For example, if a rotationally-symmetric aspheric shape is required, themembrane should inflate into either an ellipsoidal or a hyperbolicshape. Such an inflation profile can be achieved by altering thethickness of the membrane in a radially symmetric manner. Any surfaceshape can be provided by an appropriate contour of thickness across thesurface of the membrane, as could be determined by one of skill in theart.

Elastic membrane deformation is given by a superposition of elongationand bending. Stiffness in general is proportional to the modulus ofelasticity. For the elongation part of deformation, it is alsoproportional to membrane thickness; the bending part is proportional tothe thickness cubed. One method of adjusting stiffness involvesadjusting thickness of the membrane along specific orientations.Thickness of the membrane may be altered by various methods, e.g., by astretching process that is orientationally specific. Another method isto deposit a layer of a coating of variable thickness, such as through aplasma deposition process. As illustrated in FIGS. 5a,b and 6 a,b,another method is to adhesively bond a second strip of membrane ofappropriate thickness along a certain meridian of the membrane. Suchapproaches place a lesser limitation on the shape of the glassescontaining the fluid lens apparatus, since any shape may be analyzed bya finite-element-based approach, the effective “long” and “short” axesidentified, and then the thickness variation applied along those axes.Alternatively, a solution may be derived for stiffness as a function ofx,y coordinates of the membrane, and this matrix of stiffnesses may beproduced by deposition of a relatively stiff coating, such as siliconoxide (SiOx).

The design of a flexible membrane with location dependent stiffness mayrequire computation of: the mechanical response of the membrane in anoval fluid lens, the surface geometry acquired by the membrane as aresult of such deformation or stretching, and the optical power of afluid lens that includes a membrane with the resulting shape, all as afunction of the volume of fluid injected into the lens. Furthermore, anumber of iterative computations may be performed in order toapproximate as closely as possible the actual shape of the flexiblemembrane and the state of defocus of the retinal image produced by suchan optic. In one example, these complex computations were performedusing an exemplary software system. The exemplary software systemcombined several different software suites, each with a differentfunction, in a way such that each piece of software inputs its resultsinto the next system.

As an example only, the following suite was used in the computationsdescribed in exemplary embodiments herein. The deformation of the fluidmembrane was modeled on COMSOL Multiphysics software, developed byCOMSOL, Inc. of Burlington, Mass. The output of the COMSOL model wasexported into MATLAB software, produced by The MathWorks, Inc. ofNatick, Mass., in order to obtain a best fit polynomial for thissurface. A second order polynomial (quadratic) was used in order tocalculate the best combination of sphere and cylinder fit for thissurface. This polynomial was then imported into ZEMAX optical modelingsoftware, produced by ZEMAX Development Corporation of Bellevue, Wash.The deformation of the fluid membrane was calculated as a function ofits x,y coordinates on COMSOL for an elliptical fluid lens in which theeccentricity was 0.8. The long diameter was 35 mm, while the shortdiameter was 28 mm. The model was run for a quadrant, taking advantageof the four-fold symmetry. FIG. 4 illustrates an exemplary deformationgradient of a flexible membrane in a fluid lens in front projection, ascomputed on the COMSOL software package according to these parameters.The contours shown in FIG. 4 demonstrate that the deformation wasnon-uniform throughout the membrane, reaching a peak of 0.7 mm (700microns) for a pressure of 2000 Pascals. FIGS. 8a and 8b each representa one-dimensional scan of the deformation shown in FIG. 4. FIG. 8arepresents the deformation along the horizontal axis, and FIG. 8brepresents the deformation along the vertical axis. Meshing was done insweep mode (extra fine) in three layers to include the bending mode,generating 5439 elements in all. This data was exported into MATLAB forthe best second order polynomial fit to be input into ZEMAX.

During the initial assessment of this computation scheme, it wasobserved that a coarser mesh size provided adequate accuracy andfidelity to the surface generated by the finer mesh size. Also, it wasfound that the cross terms could be neglected in the second orderpolynomial best fit computed on MATLAB, so that the surface could beadequately represented as a simpler biconic with quadratic terms in xand y, as shown in Eqs. 3 and 4. Eq. 3 is the Best Fit equation used byMATLAB to fit the deformation data exported from COMSOL.

$\begin{matrix}{{{biconic}\mspace{14mu} {Zernike}{\mspace{11mu} \;}{sag}}{{z_{bZ}\left( {x,y} \right)}:=\left\lbrack {\frac{\frac{x^{2}}{- R_{x}} + \frac{y^{2}}{- R_{y}}}{1 + \sqrt{\begin{matrix}{1 - {\left( {1 + k_{x}} \right) \cdot \left( \frac{x}{R_{x}} \right)^{2}} -} \\{\left( {1 + k_{y}} \right) \cdot \left( \frac{y}{R_{y}} \right)^{2}}\end{matrix}}} + {\alpha_{x} \cdot x} + {\alpha_{y} \cdot y}} \right\rbrack}} & \left( {{Eq}.\mspace{14mu} 3} \right)\end{matrix}$

Eq. 4 is Eq. 3 after ignoring x,y cross terms that provided asatisfactory fit to the deformation data. This equation was used toexport surface deformation data into ZEMAX.

$\begin{matrix}{{{biconic}\mspace{14mu} {sag}}{{z_{b}\left( {x,y} \right)}:=\frac{\frac{x^{2}}{- R_{x}} + \frac{y^{2}}{- R_{y}}}{1 + \sqrt{1 - {\left( {1 + k_{x}} \right) \cdot \left( \frac{x}{R_{x}} \right)^{2}} - {\left( {1 + k_{y}} \right) \cdot \left( \frac{y}{R_{y}} \right)^{2}}}}}} & \left( {{Eq}.\mspace{14mu} 4} \right)\end{matrix}$

This computational and modeling approach was used to evaluate differentdesign concepts for a non-round fluid lens that could be adjusted inpower over a diopter range of 2.0 D. The lower power was assumed to be1.25 D and the higher power was taken as 3.25 D. A further assumptionwas that a maximum of 0.18 D of astigmatism may be allowed at the lowerpower, while a maximum of 0.50 D of astigmatism was allowable at thehigher power.

In an embodiment, non-uniform thickness of the flexible membrane isprovided in order to modulate and alter its deformation in response tofluid injection and consequent increase in spherical power. A flexiblemembrane of variable thickness may be obtained in several ways, asdescribed above. In an embodiment, a tape or pad is used to alter thethickness over certain portions of the membrane surface. Such tapes orpads may be cut out of the same polymer film as that used to fabricatethe flexible membrane, and then be bonded to the flexible membrane. Forexample, the tapes or pads may be bonded to the inner surface of theflexible membrane, in contact with the fluid (e.g., oil) in order tominimize the visibility of the tapes or pads. The bonding of these tapesor pads to the membrane may be accomplished using an adhesive. In anembodiment, the adhesive has a refractive index approximately equal tothe refractive index of the fluid. Alternatively, the tapes or pads maybe bonded to the flexible membrane by laser welding or ultrasonicwelding, or other means as would be known to those of skill in the art.One or more such tapes or pads may be used for this purpose. In anembodiment, tapes and pads are not used to add thickness to the flexiblemembrane; rather, differences in thickness are integral to a singleflexible membrane sheet. Techniques for creating a flexible membrane ofvarying thickness include, for example and without limitation, molding,compression molding, thermal forming, and laser ablation.

FIGS. 5a,b and 6 a,b illustrate exemplary designs of tapes and padsmodeled to deduce the optimum shape and contours so as to modulate thestiffness of the membrane. FIGS. 5a and 5b illustrate tapes 502, 504applied along x and y axes, respectively, of a flexible membrane 506.FIGS. 6a and 6b illustrate pads 602, 604 applied along x and y axes,respectively, of a flexible membrane 606.

Table 2 shows the results of analysis of the exemplary designs shown inFIGS. 5a,b and 6 a,b, comparing the application of a tape or a pad(referred to in Table 2 as a reinforcing piece) along x and y axes. Inthe exemplary model used in Table 2, the thickness of the reinforcingpiece (e.g., tape or pad) was the same as that of the flexible membraneitself. That is, the thickness was doubled where reinforcement wasapplied. The final analysis was performed on ZEMAX software that wasused to compute the astigmatism over the entire range of sphericalpowers, as well as the image spot size along x and y axes. In thisanalysis, the eccentricity as been assumed to be 0.864, the optic being35 mm along the long axis (x axis) and 30.25 mm along the short axis (yaxis). The lowest optical power is 1.25 D and the highest optical poweris 3.25 D. The front surface of the rigid lens has been provided with atoric correction such that the net astigmatism at the lowest power (1.25D) is 0.18 D in all cases. Spot size along the x axis is when focusedfor x; spot size along the y axis is when focused for y.

TABLE 2 Modeling of reinforcing piece on flexible membrane in anelliptical fluid lens Reinforcing Astigmatism at Spot size along x Spotsize along y Piece 3.25 D axis, Microns axis, Microns None 0.73 D 10.114.2 Pad along x axis 0.61 D 9.9 13.2 (FIG. 5a) Pad along y axis 1.02 D10.6 16.9 (FIG. 5b) Tape along x axis 0.51 D 9.7 12.5 (FIG. 4a) Tapealong y axis 1.04 D 10.4 17.0 (FIG. 4b)

Next, the effect of increasing reinforcement was examined as a functionof eccentricity. Table 3 shows the rate of build-up of astigmatism asthe thickness of the reinforcing means was increased in an exemplarymodel. In this exemplary analysis, the eccentricity was assumed to be0.864, with the long diameter being 35.0 mm. The lowest and the highestspherical powers were assumed to be 1.25 D and 3.25 D, respectively,with the range of adjustment being 2.0 D. It was also assumed that thefront surface of the rigid optic was provided with toric correctionalong the appropriate axis, so that the net astigmatism at the lowestpower is held at 0.18 D. Astigmatism at the highest spherical power wascomputed on ZEMAX, along with the spot size of the image. The basemembrane was assumed to be of unit thickness, so that a reinforcingpiece of 1× thickness doubles the thickness of the membrane where it wasapplied. It is expected that the spot size of the image would becorrelated with the point spread function of the retinal image, acritical measure of the crispness and clarity of the retinal image, anda measure of the image quality perceived by the wearer. In the exampleshown in Table 3, there was an improvement in image quality as thethickness of the reinforcement was increased in the fluid lens.

TABLE 3 Change in astigmatism as a function of reinforcement thicknessMax Reinforcing Astigmatism at Spot size along x Spot size along y Piece3.25 D axis, Microns axis, Microns None 0.73 D 10.1 14.2 Pad 1X 0.61 D9.5 13.2 Pad 2X 0.37 D 7.5 9.4 Pad 3X 0.14 D 7.4 8.0 Tape 1X 0.51 D 9.712.5 Tape 2X 0.35 D 9.5 11.4 Tape 3X 0.17 D 9.2 10.2

It was found in this example that the 3× reinforcement enabled the useof a non-round optic up to eccentricities of 0.80 while staying withinthe limits of astigmatism specified for the lowest and the highestspherical powers (sph) (e.g., 0.18 D at 1.25 sph and 0.50 D at 3.25 Dsph). This level of eccentricity is adequate for most lens designs,since it provides a long axis diameter of 40 mm for a short axisdiameter of 32 mm. Further departures from the round shape (e.g., aneccentricity of 0.7) can be achieved by enhancing the reinforcementfurther, for example by using a pad or a tape that is 4×-6× inthickness.

It should be noted that the analysis and results presented aboveaddressed an exemplary paraxial situation assuming a pupil size of 4.0mm. In other words, it was applicable to the center of the optic over amoderate field angle, less than 10 degrees. This analysis may berepeated at different gaze angles for the whole optic. Such acomputation would further optimize the shape of the membrane, since itwould be possible to prescribe reinforcing schemes that provide the bestcorrection for the whole optic, rather than providing the bestcorrection at the optical center. In performing this globaloptimization, it may be recognized that the optical segments far fromthe center are not as important in determining overall visualsatisfaction as the center of the optic, since most viewing tasksrequire direct gaze with controlled eye movements that supplement headmovements for the most comfortable near-vision experience.

Other shaped optics, such as rectangular- or square-shaped optics, mayalso be adapted to this approach. The shape of the deformed membrane maybe described, for example, as a collection of points such as a pointcloud, or a collection of splines used to fit the points. In this case,the wavefront of rays transmitted through the liquid lens (including thedeformed membrane) is computed, and an adaptive correction may beapplied to the wavefront to maximize the retinal image quality. Theretinal image quality may be measured by one of the severalcommonly-used metrics of image quality, such as the Strehl ratio or theequivalent defocus.

Fluid Lens Inset

In an inset-type design embodiment, the non-round shape of the fluidlens includes a round or elliptical section centered at the location ofthe pupil of the wearer. In such an embodiment, upon putting on theglasses, the center of the pupil lines up with the center of the inset.With a circular inset, the active region may be small depending on theshape of the lens frame, because the vertical diameter of the circularshape must fit within the vertical diameter of the frame. If the activeregion of the flexible membrane is too small, it may be unsuitable for awearer as the eye movement of a wearer may need a larger viewing rangeside-to-side than up-to-down. For example, an average wearer needs anactive area width of about 30-35 mm for comfortable side-to-side eyemovement. An elliptical inset portion allows for such an active areawidth, even when the vertical dimension of the inset is small comparedto the active area width. FIGS. 7a,b illustrate an exemplary ellipticalinset 702 in a fluid lens assembly 704. The inset optic 702 is referredto herein as the active optical region. The active optical region isdesigned to inflate to deliver the desired power range. Thespecifications of astigmatism at the low and high end of the power rangeapply to the active region only. The active region may be developed bycontouring the thickness of the membrane to be substantially thinnerthan in the surrounding optical region. For example, as shown inexemplary elliptical inset 702 of FIG. 7b , it was found that for anactive region of 25 mm×35 mm, an eccentricity of 0.80 met the opticalspecifications mentioned above over a power range of 1.50 D, from 1.25 Dto 2.75 D. A membrane thickness ratio of 2× to 10× may be used providethis segmentation of the overall optical area. In an embodiment, themembrane thickness ratio is 3× to 7×. The smaller the thickness ratio,the more deflection is experienced by the outer zone. This leads to ahigher level of astigmatism in the active zone.

For such a design to be cosmetically acceptable, the border of theactive optical region may be smoothly blended, so that image jump orperceivable image distortions are avoided. It is found that the maincauses of the visual discomfort associated with this border are: (1)prism discontinuity; (2) magnification discontinuity; and (3) highlocalized astigmatism, caused by power discontinuity. These are also themain factors that contribute to the visibility of this border,potentially leading to a cosmetically unacceptable outcome. Theseproblems may be minimized by providing a transition zone. In anembodiment, the transition zone is approximately 1-5 mm in width. In afurther embodiment, the transition zone is approximately 2-3 mm inwidth. The width of the transition zone may be determined by thegradient in power within this zone, since visual performance of thiszone may be acceptable, for example, only for a power gradient of 0.50D/mm or less, leading to a maximum value of astigmatism of 0.50 D atthis zone. In such an example, a power range of 1.50 D requires atransition zone of 3.0 mm in width.

CONCLUSION

While various embodiments of the present invention have been describedabove, it should be understood that they have been presented by way ofexample only, and not limitation. It will be apparent to persons skilledin the relevant art that various changes in form and detail can be madetherein without departing from the spirit and scope of the invention.Thus, the breadth and scope of the present invention should not belimited by any of the above-described exemplary embodiments, but shouldbe defined only in accordance with the following claims and theirequivalents.

Further, the purpose of the foregoing Abstract is to enable the U.S.Patent and Trademark Office and the public generally, and especially thescientists, engineers and practitioners in the art who are not familiarwith patent or legal terms or phraseology, to determine quickly from acursory inspection the nature and essence of the technical disclosure ofthe application. The Abstract is not intended to be limiting as to thescope of the present invention in any way.

What is claimed is:
 1. A fluid lens assembly, comprising: a non-roundrigid lens having a back surface and a front surface, the front surfacehaving a rotationally symmetrical aspheric correction; a flexiblemembrane coupled to the back surface of the non-round rigid lens, suchthat a cavity is formed between a front surface of the flexible membraneand the back surface of the rigid lens; and a reservoir in fluidcommunication with the cavity between the front surface of the flexiblemembrane and the back surface of the non-round rigid lens, such that afluid is transferable between the reservoir and the cavity to change theoptical power of the fluid lens assembly, wherein the front surfacehaving a rotationally symmetrical aspheric correction at least partiallyreduces an optical error, and wherein the rotationally symmetricalaspheric correction does not exceed 0.18 D.
 2. The fluid lens assemblyof claim 1, wherein the fluid lens assembly is within a pair ofeyeglasses, and wherein the front surface having a rotationallysymmetrical aspheric correction at least partially reduces a plus powerof the fluid lens at certain gaze angles.
 3. The fluid lens assembly ofclaim 1, wherein the front surface having a rotationally symmetricalaspheric correction at least partially reduces a spherical aberrationoptical error.
 4. The fluid lens assembly of claim 1, wherein the frontsurface is ellipsoidal.
 5. The fluid lens assembly of claim 1, whereinthe front surface is hyperboloidal.
 6. A fluid lens assembly,comprising: a non-round rigid lens having a back surface and a frontsurface, the front surface having a toric aspheric correction; aflexible membrane coupled to the back surface of the non-round rigidlens, such that a cavity is formed between a front surface of theflexible membrane and the back surface of the rigid lens; and areservoir in fluid communication with the cavity between the frontsurface of the flexible membrane and the back surface of the non-roundrigid lens, such that a fluid is transferable between the reservoir andthe cavity to change the optical power of the fluid lens assembly,wherein the front surface having a toric aspheric correction at leastpartially neutralizes astigmatism generated on the flexible membrane byinflation of the flexible membrane, and wherein the toric asphericcorrection does not exceed 0.18 D.
 7. The fluid lens assembly of claim6, wherein the fluid lens assembly is within a pair of eyeglasses, andwherein the front surface having a toric aspheric correction at leastpartially neutralizes natural astigmatism of an eye of a wearer of thefluid lens assembly.
 8. A fluid lens assembly, comprising: a non-roundrigid lens having a back surface and a front surface, the front surfacehaving a toric aspheric correction; a flexible membrane coupled to theback surface of the non-round rigid lens, such that a cavity is formedbetween a front surface of the flexible membrane and the back surface ofthe rigid lens; and a reservoir in fluid communication with the cavitybetween the front surface of the flexible membrane and the back surfaceof the non-round rigid lens, such that a fluid is transferable betweenthe reservoir and the cavity to change the optical power of the fluidlens assembly, wherein the front surface having a toric asphericcorrection at least partially neutralizes astigmatism generated on theflexible membrane by inflation of the flexible membrane, and wherein aneccentricity of the fluid lens is approximately 0.94.
 9. The fluid lensassembly of claim 6, further comprising a second flexible membraneattached to the front surface of the flexible membrane.
 10. The fluidlens assembly of claim 9, wherein the second flexible membrane is bondedto the front surface of the flexible membrane with an adhesive.
 11. Thefluid lens assembly of claim 10, wherein the adhesive has a refractiveindex approximately equal to a refractive index of the fluid.
 12. Thefluid lens assembly of claim 9, wherein the second flexible membrane isbonded to the front surface of the flexible membrane by laser welding.13. The fluid lens assembly of claim 9, wherein the second flexiblemembrane is bonded to the front surface of the flexible membrane byultrasonic welding.
 14. The fluid lens assembly of claim 9, wherein athickness of the second flexible membrane is approximately equal to athickness of the flexible membrane.
 15. The fluid lens assembly of claim9, wherein a thickness of the second flexible membrane is approximatelythree times larger than a thickness of the flexible membrane.
 16. Thefluid lens assembly of claim 9, wherein a thickness of the secondflexible membrane is approximately four times larger than a thickness ofthe flexible membrane.
 17. The fluid lens assembly of claim 9, wherein athickness of the second flexible membrane is approximately six timeslarger than a thickness of the flexible membrane.
 18. The fluid lensassembly of claim 9, wherein a thickness of the second flexible membraneis approximately four to six times larger than a thickness of theflexible membrane.